Dynamic rough set learning for reliable early warning in industrial time-series systems.

Industrial early-warning systems require models that can detect transitional risk states before failure while also explaining uncertainty in the resulting decisions. Existing machine-learning and deep-learning approaches can achieve strong predictive performance, but they often provide limited information about whether a time-series window is certainly normal, certainly critical or only ambiguously classified. This paper addresses this problem by proposing a dynamic rough set learning framework for uncertainty-aware early warning in industrial time-series systems. The proposed method converts multivariate sensor trajectories into sliding-window decision systems and constructs time-dependent neighborhood rough approximations for evolving decision classes. A rough early-warning index is introduced to quantify boundary-region expansion over time, and a dynamic dependency-based feature-reduction procedure is developed to retain informative window descriptors while preserving rough decision ability. Unlike purely black-box classifiers, the framework provides class predictions together with support gaps, local uncertainty scores, boundary-region information, deferred decisions and warning rates. The framework is evaluated on the NASA C-MAPSS FD001 turbofan degradation benchmark. The full dynamic rough set model achieves a test accuracy of 0.8647, balanced accuracy of 0.7570 and Macro-F1 score of 0.7895. Random Forest and XGBoost obtain stronger pure classification scores, with Macro-F1 values of 0.8715 and 0.8611, respectively. However, the proposed method supplies additional rough uncertainty outputs that are useful for inspecting transitional and ambiguous windows. Dynamic rough feature reduction decreases the feature set from 118 to 40 features while retaining a test accuracy of 0.8459 and Macro-F1 score of 0.7564. Robustness analysis further shows that the model is stable under moderate Gaussian feature noise, whereas high missingness mainly affects the warning class. These findings indicate that the proposed framework is most suitable for early-warning settings where interpretability, uncertainty qualification and inspection prioritization are as important as raw classification accuracy.